In a train yard there are 4 tank cars, 12 boxcars, and 7 flatcars. How many ways can a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars if their order make no difference.

The trian can be made up in 166,320 ways.

Step-by-step explanation:

The order makes no difference, which means that we use the combinations formula to solve this problem.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

We are going to choose

2 tank cars from a set of 4

5 boxcars from a set of 12

3 flatcars from a set of 7

How many ways can a train be made up?

Multiplication of the number of possibles sets of tanks, boxcars and flatcars. So

The trian can be made up in 166,320 ways.

The number of ways is 166,320ways

If there are "n" objects, the number of ways of selecting r objects is expressed as:

If there are 4 tank cars, 12 boxcars, and 7 flatcars in a train yard, the number of ways a train be made up consisting of 2 tank cars, 5 boxcars, and 3 flatcars is expressed as:

Hence the number of ways is 166,320ways

Learn more on combination here: link

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

the answer will be